The other day I was interested in learning benefits (and possible negatives) of launching a rocket via a plane like that which is used by scaled composites versus a ground launched VTVL approach such as that advocated by AA.

My expectation was that launching a rocket plane gives the "best of both worlds" whereby you get the benefits of an air breathing plane in the thicker atmosphere of lower altitudes and an outperforming rocket engine that can accelerate much quicker than if launched from the ground. Let’s face it - on the surface the whole challenge of rocket propulsion is that it takes a huge amount of force to actually get a vehicle up there and wouldn’t starting a little closer to the finish line help a lot?

What I found, however, was not what I expected.

To do my analysis I used equation 4-16 from Rocket Propulsion Elements, 8th Edition (Sutton and Biblarz) to calculate final cutoff velocity (vf) and then solve for distance.

Using data publicly available from the scaled composites 2004 flights (I would have preferred to use AA data were it available) I found that a Rocket Propelled Plane launched at 45000ft (13,716 meters) with an initial velocity of 59 m/sec (215 kph) reaches a max altitude of approximately 106.7km (13.7km launch height + 93km climb).

The same rocket engine launched vertically from the ground would obtain a max altitude of approximately 82km or 24.7km less than the air launched plane.

Subtracting the 13.7km launch height advantage of the Rocket plane means that an air launch gained only an aggregate 11km in altitude versus the ground launch. This is clearly not a lot.

In fact looking at these numbers further I found that the ground launched plane would need roughly 10% more Force to match the performance of its air-launched counterpart.

Not exactly a huge advantage if you ask me.

While this simple analysis doesn’t take into account drag or the different flight vectors of a vertically versus air-launched vessel, however, it does raise some interesting questions mainly: “what exactly are the benefits of a space plane?”

Without further analysis I can’t say for certain but I’d suspect the high-drag re-entry, which uses almost no rocket propulsion is a huge plus. This in comparison to the relatively small but still significant force needed to slow down an AA engine via retro-rockets. There is also a reusability argument but I think both organizations do this pretty well so I won’t try to raise any new points there.

While the effect of drag was purposely excluded in the above example it probably would become a more significant factor in a real-world test. Particularly, because the air-launched plane was deployed where pressure was significantly less then on the earth’s surface the effect of drag would also be much less. This would allow the air launched rocket to accelerate much faster than its ground based counterpart.

Anyway this all got me thinking so I thought I’d throw it out there to get some more insight.

What do you think?

Do the benefits of space planes really outweigh those of their ground based counterparts?

It's not just about performance. With a carrier plane, you can fly around any adverse weather, or, for orbital launches, fly to a more advantageous launch point closer to the equator. Also, if something goes wrong with the spacecraft, you can glide back to the ground and you have some time to figure out the problem and get down safely. If you launch from the ground and something goes wrong in the first few seconds, then that's pretty much it, you don't have enough altitude to recover.

On the other hand, a modular rocket has advantages of economy. You can make lots of modules, and take advantage of efficient mass production, since all your craft are the same. It's hard to imagine more than a handful of WK2s ever being built (one for each launch location), with maybe twice as many SS2s, while a hundred or so AA modules is not so much of a stretch. Commonly used sounding rockets go up to 300 to 400km, for which I'd guesstimate you need tens of the current modules.

_________________Say, can you feel the thunder in the air? Just like the moment ’fore it hits – then it’s everywhereWhat is this spell we’re under, do you care? The might to rise above it is now within your sphereMachinae Supremacy – Sid Icarus

So I read Jonathan’s articles on orbital access methodologies and I have to say it was well worth the time. Actually it was an extremely good read and I spent way way more than an hour with these thanks again Trance for the recommendation!

If you haven’t read them and are interested in some not too techie thoughts on cost-conscious ways to access space I would (also) highly recommend them.

The main point I took from Jonathan’s articles is that to cover any significant distance you have to look at TSTO (Two Stage to Orbit) propulsion designs and then it becomes a matter of figuring out how to cost-effectively get the first & second stages back.

Jonathan used the cutoff velocity equation (this is the same one I used in my first post) to rationalize this. His line of thinking is that because there is an exponential relationship between mass-ratio and cutoff velocity dropping as much of that weight as possible via staging is highly desirable.

This also got me thinking about the benefits of staging versus not staging so I decided to take my basic model for cutoff velocity and refine it to calculate more closely the effect of average gravitational attraction as the distance from the earth’s surface increases.

Then I used these values to derive distance and acceleration, mashed the whole thing up and basically figured out how far a rocket engine would go. These analyses lead me to 3 conclusions:

1) Mass Ratio is absolutely without a doubt the most important factor in space flight. Adding more propulsion, if it is equivalent to mass, yields literally no gain final velocity. Obviously there is a benefit to payload capacity but it just serves to re-highlight the “lower-end” opportunities of private space flight.2) Unless you have a really good mass ratio it’s pretty hard to get more than a few thousand kilometers up. 3) Staging seemed to provide about a 33% performance boost over an equivalent non-staging flight (eg. same characteristic velocity, propellant mass fraction and burn time).

Conclusion 1 - I used a propellant mass fraction of 90% for 2 flights. The first at 90 kg of propellant and 10kg of dry mass and the second at 90,000 kg of propellant and 10,000 kg of dry mass. All other variables were kept the same. Both yielded the exact same cutoff velocity albeit with the later vehicle having a much larger payload capacity.

Conclusion 2 -This can be inferred by simply looking at the first part of the equation for cutoff velocity ln(1-mf) but it takes plugging in a few numbers for it to really sink in that it’s basically impossible to launch a vehicle beyond a few hundred km unless you have a propellant mass fraction of at least 90%. Even with this you’ll need a pretty decent specific impulse to start getting up to 5,000 km or greater. And unless you have a superb specific impulse and mass ratio you aren’t going to get much further than that.

Conclusion 3 -To come up with my 33% number I took a relatively simple scenario: 1 rocket with 90 kg of propulsion and 10 kg of dry mass firing for 180 seconds with a 2943 m/sec characteristic velocity (essentially a 300 Specific Impulse). As a single stage the cutoff velocity was 5177 m/sec.

For the 2 stage scenario I took the same variables and split them between the stages. For stage one I arbitrarily chose 60 kg of fuel mass (Mass Fraction of 60%) firing for 90 sec or half the burn time of its single stage counterpart. The first stage resulted in a cutoff velocity of 1858 m/sec.

For the second stage I took the remaining fuel 30 kg (100kg total - 65kg 1st stage - 5kg dry mass second stage) firing for the other 90 seconds, which resulted in a final velocity of 6933 m/sec or a 33% improvement over its single stage counterpart.

I’ll confess I didn’t look at this in too much depth but given the argument that staging provides a significant bonus to vehicle velocity I’m really curious to know more.

In particular, the number one question on my mind is what ratio of propellant mass fraction per stage gives the best total velocity? Also, what sort of performance boost does each stage give? I’m sure this tails off at some point but it would be really interesting to analyze the effect of 2 vs 3 or more stages.

Anyway… that’s enough of me blabbing.

Do you agree with this analysis? How can mass fractions be allocated to provide the optimal cutoff velocity when staging?At what point do stages cease to be useful?

-Graham

ps – I’m more than happy to share the math behind these conclusions if anyone is interested. Just let me know.